I can't speak Japanese, only some Chinese, but I'm wondering if whether to use the (Chinese) Onyomi or (Japanese) Kunyomi pronunciation in Japanese is related in any way to whether the 山 comes first or last in the compound. If it comes last as in 富士山 "Fuji san", the grammar matches the Chinese, and so does the pronunciation ("Fushishan"). If it comes first as in 山登り "yamanoboru", the grammar is opposite to the Chinese (which would also have the 山 last, i.e. 跑山).

PS: Isn't り pronounced "ri" and る pronounced "ru"?